Some Cryptographic Properties of Rotation Symmetric Boolean Functions

Using the derivative of H Boolean functions and the e-derivativedefined by the authors as the research tools, we go deep into the internal structure of the Booleanfunction values​​, additionally,by the methods of cascade calculations and analytic combinatorics, cryptographic properties such as structural features, existence,balance and algebraic immunity of rotation symmetric H Boolean functions withdiffusibility are studied. Then we get the results that the Second Order rotation symmetric Boolean functionsare H Boolean functions,andthe results to the issues such asthe balance and algebraic immunity of rotation symmetric H Boolean functionsand the existence of the Third Order symmetric H Boolean functions are also be established.